A253000 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

1, 1, 1, 1, 69, 1132, 7235, 25233, 63135, 129133, 231419, 378185, 577623, 837925, 1167283, 1573889, 2065935, 2651613, 3339115, 4136633, 5052359, 6094485, 7271203, 8590705, 10061183, 11690829, 13487835, 15460393, 17616695, 19964933, 22513299

Offset

1,5

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (4096/3)*n^3 - 22816*n^2 + (388490/3)*n - 249567 for n>6.

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 68*x^4 + 859*x^5 + 3118*x^6 + 2810*x^7 + 1154*x^8 + 183*x^9) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.

(End)

Example

Some solutions for n=6:
..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..1..1..2
..0..0..0..1....1..1..1..1....0..1..1..1....0..1..1..1....1..1..1..2
..0..1..1..1....1..1..2..2....1..1..1..2....1..1..2..2....1..1..1..2
..0..1..2..2....1..1..2..2....2..2..2..2....1..2..2..2....1..1..1..2
..1..1..2..2....1..2..2..2....2..2..2..2....1..2..2..2....1..1..1..2
..2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2

Crossrefs

Column 4 of A253004.

Sequence in context: A160831 A254683 A095255 * A295212 A264283 A333034

Adjacent sequences: A252997 A252998 A252999 * A253001 A253002 A253003

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved